HOUSTON (CBS Houston) – You have to respect Texans rookie quarterback Case Keenum and his hustle when it comes to how he sees himself fitting in with his new team.

It’s been understood since the Texans signed Keenum as an undrafted free agent out of University of Houston this past spring that he would compete for the team’s third quarterback spot on the roster. And that is exactly the situation Keenum finds himself this training camp, trying to gain ground on sixth-year veteran John Beck to become the team’s third-string quarterback.

But when asked by a reporter this week why Keenum thought he should be the Texans third string quarterback, there was this awkward pause.

“That’s a tough question because I don’t think anybody wants to be the third string (quarterback),” Keenum finally responded. “I’m not concentrating on that. I’m out here trying to get better every day but I don’t want to just be a backup. That’s not my ultimate goal.

“I feel like I can contribute and play in this league and that’s what I want to do.”

But before Keenum can serve notice on Texans starter Matt Schaub and second-year quarterback T.J. Yates, who will be the backup, he must first make the team. A few weeks ago, that seemed like a distant dream for college football’s most prolific passer.

It’s becoming more and more realistic that they guy who has been labeled too small and who’s arm supposedly isn’t big enough to translate to the NFL game could enter the season on the Texans active roster spot.

Still, Keenum has much work to do to prove to the coaching staff and the Texans brass that they could trust him in a pinch to lead a team many believe could end up in the Super Bowl. He will get his first taste of real NFL action Saturday when the Texans travel to take on the Carolina Panthers in their preseason opener.

Keenum and his desire to get better have already impressed Texans coach Gary Kubiak. How he handles himself in live game situations will determine whether it’s him or Beck who gets to stay.

“Man, he has made a lot of progress. I guess I’m giving him a hell of a compliment but I’ve told you guys all along, football is important to him. He really works at it,” Kubiak said. “I really like the way he’s responded to his opportunity here in Houston. I think we’re all excited to see him play.”

Keenum has certainly been one of the biggest surprises in training camp, turning what seemed like a foregone conclusion a month ago into a heated competition between himself and Beck. It was assumed when that Beck would be the Texans third quarterback when he was acquired as a free agent in May after having played in similar offense under Mike Shanahan with the Washington Redskins.

If Keenum had any chance at all with the Texans it was going to be as a practice squad player this season. But Keenum has been impressive enough that he and Beck have rotated the limited snaps afforded the third string quarterback. And at times it has appeared Keenum has moved past Beck been then there are moments he tries to force things and throw an interception and he quickly finds out how thin the line between third string and odd man out is.

“I’ve been working really hard. Just trying to attack each day and grind out each rep,” Keenum said. “I think it’s a deal where you got to take every rep whether you’re in there or not as a mental rep.”

The same can be said for Beck, who has continued the inconsistency traits that relegated him from part-time starter with the Redskins to being out the door this offseason. Kubiak wants to see improvement from Beck and soon.

Otherwise Beck could be the next veteran who has his spot taken by an unproven rookie.

“He’s (Beck) a veteran payer in a system that he should be comfortable with,” said Kubiak, who confirmed Beck would see action before Keenum on Saturday but that could change next week. “I think he could be doing better than he’s doing right now. I would tell him the same thing, but now it’s time to go play and see. He’s gotten a ton of reps.

“To me, I told him he came here to compete with T.J. and Case. I think he’s doing that but I think there’s another level for him to reach. He’s been playing enough football that he should step on that field and be comfortable Saturday.”

In the meantime, Keenum is waiting and quite frankly feeling he has nothing to lose as undrafted free agent that few outside of these city limits expected much from.

“I think I’ve played that way my whole life. It’s got to be that way,” he said. “You got to play like you have nothing to lose. I just know that at the end of it, I’m going to give it my all each day and just try to get as much out each rep and each day as I can.”